Question: Alexandra played 15 games of Skee Ball for $\$11.25.$ After each game, she earned either 2 tickets or 4 tickets. At the end of 15 games she had earned a total of 40 tickets. For how many games did she earn 4 tickets?
Explanation: Imagine taking 2 tickets away from Alexandra after each game. Then she earned either 0 or 2 tickets each time, earning a total of $40 - 2\cdot 15 = 10$. So under this new scheme, she won two tickets 5 times, meaning originally she earned four tickets on $\boxed{5}$ games.